Quantized bound states around a vortex in anisotropic superconductors  

作　　者：Ke Xiang Da Wang Qiang-Hua Wang 

机构地区：[1]National Laboratory of Solid State Microstructures&School of Physics,Nanjing University,Nanjing 210093,China [2]Collaborative Innovation Center of Advanced Microstructures,Nanjing 210093,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2024年第6期146-155,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Key R&D Program of China(Grant No.2022YFA1403201);the National Natural Science Foundation of China(Grant Nos.12274205,12374147,92365203,and 11874205)。

摘　　要：The bound states around a vortex in anisotropic superconductors is a longstanding yet important issue.In this work,we develop a variational theory on the basis of the Andreev approximation to obtain the energy levels and wave functions of the low-energy quantized bound states in superconductors with anisotropic pairing on arbitrary Fermi surface.In the case of circular Fermi surface,the effective Schr¨odinger equation yielding the bound state energies gets back to the theory proposed by Volovik and Kopnin many years ago.Our generalization here enables us to prove the equidistant energy spectrum inside a vortex in a broader class of superconductors.More importantly,we are now able to obtain the wave functions of these bound states by projecting the quasiclassical wave function on the eigenmodes of the effective Schr¨odinger equation,going beyond the quasiclassical Eilenberger results,which,as we find,are sensitive to the scattering rate.For the case of isotropic Fermi surface,the spatial profile of the low-energy local density of states is dominated near the vortex center and elongates along the gap antinode directions,in addition to the ubiquitous Friedel oscillation arising from the quantum inteference neglected in the Eilenberger theory.Moreover,as a consequence of the pairing anisotropy,the quantized wave functions develop a peculiar distribution of winding number,which reduces stepwise towards the vortex center.Our work provides a flexible way to study the vortex bound states in the future.

关 键 词：vortex bound state anisotropic superconductor Andreev approximation 

分 类 号：O469[理学—凝聚态物理]